Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron, FE/FG. Note: k = 8.99 × 109 N-m2

Question

Determine the ratio of the electrostatic force to the gravitational force between a proton and an electron, FE/FG. Note: k = 8.99 × 109 N-m2/C2; G = 6.672 × 10–11 N-m2/kg2; me = 9.109 ×

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Thành Đạt 3 years 2021-09-05T13:32:20+00:00 2 Answers 192 views 0

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  1. Helga
    0
    2021-09-05T13:33:20+00:00
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    Answer:

    \frac{F_e}{F_g} = 2.3 \times 10^{18}

    Explanation:

    The gravitational force is given by Newton’s Law of Gravity:

    F_g = \frac{Gm_1m_2}{r^2}

    The electrostatic force is given by Coulomb’s Law:

    F_e = \frac{kq_1q_2}{r^2}

    The ratio between these two forces is

    \frac{F_e}{F_g} = \frac{\frac{kq_1q_2}{r^2}}{\frac{Gm_1m_2}{r^2}} = \frac{kq_1q_2}{Gm_1m_2} = \frac{(8.99\times 10^{-12})(1.6\times 10^{-19})(1.6 \times 10^{-19})}{(6.67\times 10^{-11})(9.1 \times 10^{-31})(1.6 \times 10^{-27})} = 2.3 \times 10^{18}

  2. thachthao
    0
    2021-09-05T13:34:06+00:00
    Reply

    Complete Question:

    Determine the ratio of the electrostatic force to the gravitational force between a proton and electron, FE/FG.

    Note : k = 8.99 × 10⁹ N.m²/C² ; G = 6.672 x 10⁻¹¹ Nm²/kg²; me = 9.109 × 10⁻³¹ kg and mp = 1.672 × 10⁻²⁷kg.

    Answer:

    FE/FG = 2.3 x 10³⁹

    Explanation:

    According to Coulomb’s law, the electrostatic force (F_{E}) between two particles is given as;

    F_{E} = k x \frac{Q_1 * Q_2}{r^2 }            ——————–(i)

    Where;

    k = electric constant = 8.99 x 10⁹Nm²/C²

    Q₁ = the charge of particle 1

    Q₂ = the charge of particle 2

    r = the distance of separation between the two particles

    Also, according to Newton’s law of gravitational force, the gravitational force (F_{G}) between two particles is given as;

    F_{G} = G x \frac{M_{1} * M_2}{r^{2} }         ——————–(ii)

    Where;

    G = gravitational constant = 6.672 x 10⁻¹¹Nm²/kg²

    M₁ = mass of particle 1

    M₂ = mass of particle 2

    r = distance of separation between the two particles

    For clarity, we will calculate F_{E} and F_{G} separately before finding their ratio.

    From the question;

    The particles are a proton (particle 1) and an electron (particle 2) with the following details;

    Q₁ = charge of proton = 1.6 x 10⁻¹⁹C

    Q₂ = charge of electron = -1.6 x 10⁻¹⁹C

    M₁ = mass of proton = mp = 1.672 × 10⁻²⁷kg

    M₂ = mass of electron = me = 9.109 × 10⁻³¹kg

    Substitute the values of k, Q₁ and Q₂ into equation (i) as follows;

    F_{E} = 8.99 x 10⁹ x \frac{(1.6*10^{-19}) * ( -1.6* 10^{-19})}{r^2 }

    F_{E} = 8.99 x 10⁹ x \frac{(2.56*10^{-38})}{r^2 }  [negative sign can be discarded]

    F_{E} = \frac{(23.01*10^{-29})}{r^2 }

    Also, substitute the values of G, M₁ and M₂ into equation (ii) as follows;

    F_{G} = 6.67 x 10⁻¹¹ x \frac{(1.672*10^{-27}) * (9.109* 10^{-31})}{r^2 }

    F_{G} = 6.67 x 10⁻¹¹ x \frac{(15.23*10^{-58})}{r^2 }

    F_{G} =  \frac{(101.58*10^{-69})}{r^2 }

    The ratio F_{E} / F_{G} is therefore;

    F_{E} / F_{G}  = \frac{(23.01*10^{-29})}{r^2 } / \frac{(101.58*10^{-69})}{r^2 }

    F_{E} / F_{G}  = \frac{(23.01*10^{-29})}{(101.58*10^{-69})}

    F_{E} / F_{G}  = {(0.23*10^{40})}

    F_{E} / F_{G}  = {(2.3*10^{39})}

    Therefore, the ratio is 2.3 x 10³⁹

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